In a mobile communication system, a Random Access Preamble is normally transmitted to a base station by a mobile terminal to initiate the random access procedure and to enable synchronization of the mobile terminal with the base station.
There are 64 preambles in each cell in the document of “3GPP TS 36.211 v1.0.0-Physical Channels and Modulation” which was published in March 2007. When initiating a random access procedure, a mobile terminal transmits one of the 64 preambles. A message is transmitted to a base station by the mobile terminal selecting a particular preamble.
Before transmitting the preamble, a mobile terminal must synchronize to the carrier frequency and the frame timing of a base station to become downlink synchronized. Although the mobile terminal is downlink synchronized, there is uncertainty when a signal transmitted by the mobile terminal arrives at the base station. This is because a mobile terminal far away from the base station will receive downlink signals with a larger delay than a mobile terminal close to the base station, and the transmitted signals in uplink will take longer time to propagate to the base station for a mobile terminal which is far away from the base station compared to the signals from a mobile terminal close to the base station. The uncertainty in round trip time causes interferences between uplink signals transmitted by different mobile terminals unless uplink synchronization is performed before data transmission in uplink.
The transmission of any of the RAPs allows a base station to estimate the time of arrival of an uplink signal. The base station can then, based on the time of arrival estimate, transmit a time advance command to a mobile terminal to ensure uplink synchronization. Hence, once a preamble is transmitted by a mobile terminal, the base station may detect which preamble has been transmitted and estimate the time of arrival.
To obtain good detection properties of the preambles, or to accurately estimate the time of arrival of the uplink signal, the set of preambles should be designed to have good autocorrelation and cross-correlation properties.
The set of RAPs in Evolved UTRA (E-UTRA) is defined from one or several root sequences. A subset of the preambles xu,v(k) is generated from the uth order root Zadoff-Chu (ZC) sequence xu(k) by cyclic shifts of a plurality of the shift increments NCS. Specifically, xu,v(k) may be generated according to the equation below:xu,v(k)=xu,v((k+vNCS)mod NZC),  (1)where v is an integer, and NZC is the length of the ZC sequence defined by:xu(k)=Wuk(k+1)/2, k=0,1, . . . , NZC−1, W=e−j2π/NZC, j=√{square root over (−1)}  (2)
The number of preambles that may be generated from a single root sequence is Npre=└NZC/NCS┘, where └n┘ denotes the largest integer not greater than n. If Npre<64, then several preamble subsets generated from different root sequences are required to obtain 64 preambles in a cell. The cross-correlation between different root sequences is small but still larger than the cross-correlation between sequences generated by a single root sequence. Thus it is beneficial for the detection performance to have Npre=64 if Npre could not be set greater.
The number of ZC sequences contained in each set of ZC sequences with length of NZC is NZC−1. If the number of root sequences for obtaining the 64 preambles of a cell is Nr, Nr=┌64/Npre┐, where ┌n┐ denotes the minimal integer not smaller than n, then the number of disjoint sets is ND=└(NZC−1)/Nr┘. Different cells in a network should make use of preambles obtained from disjoint sets of root sequences, so that the base station knows whether a transmitted preamble is intended for a certain cell or not. The larger the number of root sequences Nr that is needed for obtaining 64 preambles in a cell, the smaller is the number of disjoint sets of RAPs ND. Thus, from network planning perspective it is desirable to have Npre=64, and if that is not possible to have as high value as possible of Npre.
A subset of preambles generated with equation (1) is a set of so-called Zero-Correlation Zone (ZCZ) sequences. The definition for a set of ZCZ sequences is as follows: a set of M sequences {dv(k)}, v=0,1, . . . , M−1, k=0,1, . . . , N−1, of length N, is said to be a set of ZCZ sequences, if all the sequences in the set satisfy the following autocorrelation and cross-correlation properties:
The periodic autocorrelation function Σk=0N−1dv(k)d*v((k+p) mod N) is zero for all p such that 0<|p|≦T, and the periodic cross-correlation function Σk=0N−1dv(k)d*w((k+p) mod N) is zero for all p such that |p|≦T (including p=0), where T is the length of the ZCZ.
A ZC sequence has ideal periodic autocorrelation, for example, Σk=0N−1xu(k)x*u((k+p) mod N) is zero for all nonzero p. Thus the set of preambles defined as cyclic shifts of the root sequence according to equation (1) is a set of ZCZ sequences, where the ZCZ length is T=NCS−1.
Based on Npre=└NZC/NCS┘, NCS should be as small as possible in order to make Npre be as great as possible. But the value of NCS should not be too small. In a base station a bank of correlators are used when receiving RAPs, so that there is one correlator for each preamble. Each correlator outputs time of arrival from 0 to T×Ts=(NCS−1)×Ts, where Ts is the symbol period of the sequence. The ZCZ property of the set of preambles implies that the correlator for any preamble will give a zero output if any other preamble is transmitted as long as the sum of the round trip time and delay spread in the cell is less than or equal to the product of the length of ZCZ and Ts (i.e., T×Ts). The maximum round trip time Tr in a cell is given by the cell radius R: Tr=2R/c, where c is the speed of light. Thus, the minimum value of the length of ZCZ and the minimum value of NCS length for a certain cell increase with the cell radius. Therefore, the value of the selected NCS should be large enough to ensure that the conditions mentioned above are satisfied.
Since the cell radius to be supported in E-UTRA is from 1 km to 100 km, and since NCS should be as small as possible for any given cell, there is a need for multiple values of NCS. The value of an NCS in a cell is broadcast to a mobile terminal by a base station. Of course, the base station may broadcast the length of ZCZ to the mobile terminal, so that the mobile terminal knows how to generate preambles. It is desirable to have as small amount of signaling as possible on the broadcast channel to save overload. Therefore, to achieve low signaling overload, there should be a limited predefined set of values of NCS or a set of lengths of ZCZ.
Currently, it is proposed in the 3GPP Tdoc “R1-071661-On construction and signaling of RACH preambles” disclosed in March 2007 that the cyclic shift increment value NCS in the cell was proposed to be signalled to the UE but there was no restriction on the values of the cyclic shift increment, which would then give a substantial amount of signalling. An alternative proposal is given in the 3GPP Tdoc “R1-071471—Outstanding issues in random access preamble design for E-UTRA” disclosed in March 2007, which is to have 11 values of NCS without specification how to select the values. Of course, it is not described in these documents how to select the lengths of ZCZ either. Currently there is no feasible scheme for selecting an appropriate limited set of ZCZ lengths, in order to ensure a small and limited signaling overload.